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A002373 Smallest prime in decomposition of 2n into sum of two odd primes.

%I A002373 M2273 N0899 #53 Feb 16 2025 08:32:25
%S A002373 3,3,3,5,3,3,5,3,3,5,3,5,7,3,3,5,7,3,5,3,3,5,3,5,7,3,5,7,3,3,5,7,3,5,
%T A002373 3,3,5,7,3,5,3,5,7,3,5,7,19,3,5,3,3,5,3,3,5,3,5,7,13,11,13,19,3,5,3,5,
%U A002373 7,3,3,5,7,11,11,3,3,5,7,3,5,7,3,5,3,5,7,3,5,7,3,3,5,7,11,11,3,3,5,3
%N A002373 Smallest prime in decomposition of 2n into sum of two odd primes.
%C A002373 See A020481 for another version.
%C A002373 a(A208662(n)) = A065091(n) and a(m) <> A065091(n) for m < A208662(n). - _Reinhard Zumkeller_, Feb 29 2012
%C A002373 Records are in A025019, their indices in A051610. - _Ralf Stephan_, Dec 29 2013
%C A002373 Note that these primes do not all belong to a twin prime pair. The first instance is a(110) = 23. - _Michel Marcus_, Aug 17 2020 from a suggestion by _Pierre CAMI_
%D A002373 D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 80.
%D A002373 N. Pipping, Neue Tafeln für das Goldbachsche Gesetz nebst Berichtigungen zu den Haussnerschen Tafeln, Finska Vetenskaps-Societeten, Comment. Physico Math. 4 (No. 4, 1927), pp. 1-27.
%D A002373 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002373 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002373 T. D. Noe, <a href="/A002373/b002373.txt">Table of n, a(n) for n = 3..10000</a>
%H A002373 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>
%H A002373 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%H A002373 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%t A002373 Table[k = 2; While[q = Prime[k]; ! PrimeQ[2*n - q], k++]; q, {n, 3, 100}] (* _Jean-François Alcover_, Apr 26 2011 *)
%t A002373 Table[Min[Flatten[Select[IntegerPartitions[2*n,{2}],AllTrue[ #,OddQ] && AllTrue[#,PrimeQ]&]]],{n,3,100}] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Aug 31 2020 *)
%o A002373 (Haskell) a002373 n = head $ dropWhile ((== 0) . a010051 . (2*n -)) a065091_list -- _Reinhard Zumkeller_, Feb 29 2012
%o A002373 (PARI) a(n)=forprime(p=3,n,if(isprime(2*n-p), return(p))) \\ _Charles R Greathouse IV_, May 18 2015
%Y A002373 Cf. A002372, A002374, A014092, A065091, A010051.
%K A002373 nonn,nice,easy
%O A002373 3,1
%A A002373 _N. J. A. Sloane_
%E A002373 More terms from _Ray Chandler_, Sep 19 2003